The purpose of this Choral Count is for students to practice counting by and to notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students will locate fractions on the number line, using their knowledge of unit fractions. Save the recorded count to compare to a count in an upcoming lesson.
Launch
“Cuenten de en , empezando en ” // “Count by , starting at .”
Record as students count. Record 4 fractions in each row, and then start a new row. There will be 4 rows.
Stop counting and recording at .
Activity
“¿Qué patrones ven?” // “What patterns do you see?”
1–2 minutes: quiet think time
Record responses.
None
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿En qué se parece contar de fracción en fracción a contar de número entero en número entero? ¿En qué es diferente?” // “How is counting by fractions the same as counting by whole numbers? How is it different?” (The top of the fraction is just like counting by whole numbers, going up by 1. The bottom of the fraction is different because it doesn’t change.)
Consider asking:
“¿Alguien puede describir el patrón con otras palabras?” // “Who can restate the pattern in different words?”
“¿Alguien quiere agregar otra observación sobre por qué ocurre ese patrón aquí?” // “Does anyone want to add an observation on why that pattern is happening here?”
“¿Están de acuerdo o en desacuerdo? ¿Por qué?” // “Do you agree or disagree? Why?”
“Es útil hablar de la parte de arriba de la fracción y de la parte de abajo de la fracción. Tenemos nombres para esas partes. La parte de abajo de una fracción se llama el denominador. Nos dice en cuántas partes iguales está partida la unidad. La parte de arriba de una fracción se llama el numerador. Nos dice cuántas de esas partes iguales están descritas. Busquen lugares en la lección de hoy en los que esa terminología les puede ayudar a explicar su razonamiento” // “This is a place where it’s helpful to talk about the top part of the fraction and the bottom part of the fraction. We have words for those parts. The bottom part of a fraction is called the denominator. It tells how many equal parts into which the whole is partitioned. The top part of a fraction is called the numerator. It tells how many of the equal parts are being described. Look for places in today's lesson where that terminology might help you explain your reasoning.”
Display the terms “denominador” // “denominator” and “numerador” // “numerator” along with their definitions, and keep them displayed throughout the lesson.
Activity 1
Standards Alignment
Building On
Addressing
3.NF.A.2.b
Represent a fraction on a number line diagram by marking off lengths from 0. Recognize that the resulting interval has size and that its endpoint locates the number on the number line.
The purpose of this activity is for students to practice identifying fractional intervals along a number line. This is Stage 2 of the center activity, Number Line Scoot. This activity encourages students to count by the number of intervals (the numerator). Students have to land exactly on the last tick mark, which represents 4, to encourage them to move along different number lines. While this activity does not focus on equivalence, it gives students exposure to this idea before they work more formally with it in the next section. In the Activity Synthesis, students relate counting on a number line marked in whole numbers to their number lines marked in fractional intervals.
It may be helpful to play a few rounds with the whole class to be sure students are clear on the rules of the game. Keep the number line gameboards for center use.
Engagement: Develop Effort and Persistence. Check in and provide each group with feedback that encourages collaboration and community. For example, check in after the first round of Number Line Scoot. Supports accessibility for: Attention, Social-Emotional Functioning
Launch
Groups of 2
Give each group of 2 students a gameboard, directions, a number cube, and at least 10 base-ten cubes.
“Ahora van a jugar un juego en el que se van a mover, de fracción en fracción, sobre diferentes rectas numéricas. Para comenzar, cada jugador pone un cubo pequeño sobre el 0 de cada recta numérica. El objetivo del juego es llevar tantos cubos como puedan hasta el 4 de cualquiera de las rectas numéricas” // “Now you will play a game where you move, by fractions, along different number lines. To start, each player places a small cube at 0 on each number line. The goal of the game is to get as many small cubes as you can to the 4 on any of the number lines.”
“Lancen el dado numérico. Usen el número que sacaron como el numerador de una fracción que tenga un denominador de 2, 3 o 4. Después muevan su cubo esa fracción sobre la recta numérica correcta” // “Roll the number cube and use the number as the numerator in a fraction with a denominator of 2, 3, or 4. Then move that fraction along the correct number line.”
Activity
10 minutes: partner work time
As they work, monitor for students who count by the numerator once they have chosen a number line.
None
Student Response
None
Advancing Student Thinking
Activity Synthesis
Display a gameboard with a marker on .
“Si yo sacara 4 y escogiera mover , ¿cómo contarían la movida?” // “If I rolled a 4, and chose to move , how would you count the move?” (I would count 1, 2, 3, 4.)
“¿Cómo supieron que se habían movido ?” // “How did you know you have moved ?” (Because each space is , so I need to move 4 times.)
Display a number line marked with only 0, 1, 2, 3, 4.
“¿En qué se parecen contar sobre esta recta numérica y contar sobre sus rectas numéricas? ¿En qué son diferentes?” // “How is counting along this number line the same as or different from counting along your number lines?” (On the whole-number line, each space is 1 so we just count 1, 2, 3, 4. On our number lines, we still count the jumps, but now each space is smaller than 1 so we need the denominator to tell us the size of each space.)
Activity 2
Standards Alignment
Building On
Addressing
3.NF.A.2.b
Represent a fraction on a number line diagram by marking off lengths from 0. Recognize that the resulting interval has size and that its endpoint locates the number on the number line.
The purpose of this activity is for students to locate a variety of fractions on the number line. Students locate on each number line fractions less than 1 and greater than 1, with the same denominator. The Activity Synthesis focuses on counting the number of unit fractions in a fraction to locate it on a number line and on how to determine whether a fraction is less than 1 or greater than 1. As they locate the fractions on the number lines, students strengthen their understanding of the meanings of the numerator and the denominator of a fraction (MP6).
MLR8 Discussion Supports. Synthesis: Some students may benefit from the opportunity to rehearse with a partner what they will say before they share with the whole class. Advances: Speaking
Launch
Groups of 2
Display the number line for fourths from Number Line Scoot.
“¿Qué saben sobre y ?” // “What do you know about and ?” (Both have 4 on the bottom. 3 is less than 4 and 6 is greater than 4. Both are some number of fourths.)
Share and record responses.
Activity
“Con su compañero, ubiquen las fracciones en cada recta numérica y contesten las preguntas sobre su trabajo” // “Work with your partner to locate the fractions on each number line and answer the questions about your work.”
4–6 minutes: partner work time
Monitor for students who locate non-unit fractions on the number line, by partitioning into equal parts of size , and then count the number of those parts.
Ubica y marca y .
Ubica y marca y .
Ubica y marca y .
Ubica y marca y
¿Cómo partiste la recta numérica cuando ibas a ubicar los números and ? Explain your reasoning.
¿Qué patrones observaste en las fracciones que ubicaste?
Student Response
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Advancing Student Thinking
If students partition the interval from 0 to 2 into fourths instead of the interval from 0 to 1 (or a similar error with another fraction), consider asking:
“Dime cómo encontraste en la recta numérica” // “Tell me how you found on the number line?”
“¿Cómo nos ayuda el denominador a partir la recta numérica?” // “How does the denominator help us partition the number line?”
Activity Synthesis
“¿Qué patrones observaron en las fracciones que ubicaron?” // “What patterns did you notice in the fractions you located?”
Consider asking:
“¿Cómo saben cuándo una fracción es menor que 1?” // “How do you know when a fraction is less than 1?”
“¿Cómo saben cuándo una fracción es mayor que 1?” // “How do you know when a fraction is greater than 1?”
“¿Cómo les ayudó contar de fracción unitaria en fracción unitaria a ubicar las otras fracciones en la recta numérica?” // “How did counting by unit fractions help you locate the other fractions on the number line?” (I counted by three times to find . I counted by as I moved along the number line, like , , , , , , to find .)
Activity 3
Standards Alignment
Building On
Addressing
3.NF.A.2.b
Represent a fraction on a number line diagram by marking off lengths from 0. Recognize that the resulting interval has size and that its endpoint locates the number on the number line.
The purpose of this activity is for students to determine how a number line is partitioned and what fraction is marked on it, with only 0, 1, and 2 labeled. Students partition, locate, and mark, but don’t label, a fraction on a number line, and then trade with a partner to determine the fraction their partner has marked. Remind students to mark but not label their partitions and their fraction, so that their partner has only 0, 1, and 2 to use to determine what fraction is on their number line.
Launch
Groups of 2
“Completen la primera parte de la actividad individualmente. Partan la recta numérica y pongan una marca que represente una fracción, pero no escriban el número. No le digan a su compañero cómo partieron la recta numérica ni qué número representa la marca” // “Complete the first part of the activity on your own. Partition the number line and mark, but don’t label, a fraction on the number line. Don’t tell your partner how you are partitioning or what number you are marking.”
2 minutes: independent work time
Activity
“Ahora intercambien rectas numéricas con su pareja y respondan las preguntas sobre la recta numérica de su compañero. Cuando ambos terminen, compartan cómo razonaron” // “Now trade number lines with your partner, and answer the questions about their number line. When you both are finished, share your reasoning”
1–2 minutes: independent work time
1–2 minutes: partner work time
Haz una partición de la recta numérica en cualquier número de partes de igual tamaño. Escoge una fracción y ubícala. Pon una marca que la represente, pero no escribas el número.
Intercambia tu recta numérica con la de un compañero.
¿Cómo partió su recta numérica tu compañero?
¿Qué número representa la marca de tu compañero en su recta numérica? Explica tu razonamiento.
Si te queda tiempo, usa las rectas numéricas para repetir la actividad.
Student Response
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Advancing Student Thinking
Activity Synthesis
Display a number line partitioned by a student.
“Hablen con su compañero sobre qué fracción está representada” // “Talk to your partner about what fraction is represented.”
Share and record responses.
Consider asking:
“¿Cómo decidieron de qué manera partir su recta numérica y qué fracción marcar?” // “How did you decide to partition your number line and what fraction to mark?”
“¿Cómo decidieron de qué manera estaba partida la recta numérica de su compañero y qué fracción estaba marcada?” // “How did you decide your partner’s number line was partitioned and what fraction was marked?”
Lesson Synthesis
“Hoy ubicamos más fracciones en la recta numérica. En una lección anterior, aprendimos cómo se construyen las fracciones a partir de fracciones unitarias. ¿Cómo vemos esto en la recta numérica?” // “Today we located more fractions on the number line. In an earlier lesson, we learned how fractions are built from unit fractions. How do we see this on the number line?” (I count the unit fractions, like 3 one-fourths to get to . I partition the number line into unit fractions, and then I can count parts up to the fraction I am locating.)
Draw, or have students draw, a number line with marked, such as:
Trace, or have them trace, and count the 3 one-fourths to get to , such as:
“Recuerden que cuando ubicamos una fracción en la recta numérica, es útil mostrar o pensar en las 3 cuartas partes. Luego, ponemos la marca y escribimos el número al final de esas partes. Cuando ubican y marcan fracciones, no tienen que marcar la longitud. Pueden simplemente contar las fracciones unitarias, y luego poner el punto al final y marcarlo” // “Remember, when we are locating a fraction on the number line, it might be helpful to think about or show the 3 one-fourth parts, and then we mark and label the number at the end of those parts. When you locate and label fractions, you don’t have to mark the length. You can just count the unit fractions, and then mark and label the point at the end.”
Point to the location of each fraction on the number line, and count: “, , .”
Standards Alignment
Building On
Addressing
Building Toward
3.NF.A.2
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
